They're calling it the Bar Removal of Individuals who Dream and Grow Our Economy Act, or BRIDGE Act.

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"This is an effort by Sen. Graham and myself to have a bipartisan answer to the question about what happens to these 800,000 and others like them while we debate the future of immigration," Durbin said.

He added that hundreds of thousands of immigrants have a "concern and a fear" about what will happen to them if Trump roles back Obama's executive action.

The DACA program — which has faced a lengthy legal battle — provides people living in the U.S. illegally who arrived as children with work authorization and a temporary halt on deportation if they meet certain requirements.

The legislation would allow undocumented immigrants who are eligible for DACA to apply for "provisional protected status" if they pay a fine and undergo a background check.

The law would sunset after three years.

"If you have DACA now you would receive provisional protected status until your DACA expires and you can apply for an extension," Durbin said.

The legislation won't pass the Senate this year, with lawmakers expected to leave town as soon as Friday. Durbin indicated Friday they would reintroduce the bill early next year.

Graham announced late last month that he was working on the bill with Durbin, arguing it would buy "Dreamers" time as lawmakers try to pass a broader comprehensive immigration bill.

"If he repeals it then we ought to immediately pass legislation to extend their legal status. I'm willing to do that," he said. "I'm going to support legislation that will continue legal status for these kids until we can find a fix to the overall program."

He added separately that the fight over the undocumented immigrants is a "very defining moment about who we are as a party."

Graham urged Trump to back the bill on Friday, arguing it would help pave the way to provide legal status through "the proper constitutional process."

The legislation comes as Trump appeared to soften his immigration stance this week, pledging to "work something out."

“They got brought here at a very young age, they’ve worked here, they’ve gone to school here. Some were good students. Some have wonderful jobs. And they’re in never-never land because they don’t know what’s going to happen," he told Time magazine.

Trump came under fire during the campaign for taking a hard-line on immigration, pledging to deport roughly 11 million undocumented immigrants. He's walked that back since, noting he would focus primarily on those with criminal records.

Friday's legislation was quickly endorsed by outside groups.

Frank Sharry, the executive director of America’s Voice, called the bill an "important step."

"It is not the broad reform that the country needs and that the American people support, but it would at least avert the disruption and heartbreak that would accompany a revocation of DACA," he said.

Ali Noorani, the executive director of the National Immigration Forum, echoed Sharry's remarks adding that the bill is "one piece of a much larger puzzle."

"We hope to work with the Trump administration and the 115th Congress to address the immigration system broadly so that it benefits all American workers, including immigrants," he said.

It's unclear if, or when, the Graham-Durbin bill could be taken up next year.

"But I don't think [Trump is] interested in hurting the children who came with their parents," he said. "They're not culpable of anything. I think there needs be a reasonable way to deal with, and I think he's indicated he's open to that."